OF SYMMETRY & HARMONY

01-May-2018

RAJGOPAL NIDAMBOOR

Symmetry is just not a word; it’s a concept. A concept that has a timeless appeal in the human mind. It not only attracts our visual sense, but it also plays more than a prominent role in our sense of beauty. Not that the idea is perfect. Far from it: a paradox too. Perfect symmetry, for instance, happens to be quite repetitive and predictable. May be, our mind also likes surprises, in a way. This explains why we often consider imperfect symmetry to be more beautiful than perfect mathematical symmetry.

The world of nature is another example: many of the most striking patterns in the natural world are symmetric. Yet, nature isn’t all too comfortable when it comes to a question of too much symmetry. Reason? Nearly all the symmetric patterns in nature are less symmetric than the causes that give rise to them. The physicist Pierre Curie put the paradox in perspective. He called it a general principle: “Effects are as symmetric as their causes.” The world, as such, is full of such effects. It has an identity of its own too: spontaneous ‘symmetry breaking.’

A mathematical and an aesthetic concept, symmetry has a pattern and something more to it than what meets the eye and mind: one that helps us to distinguish between them. Take the human body, for example. Our body is bilaterally symmetric; its left half is almost the same as its right-half. In simple terms, it is approximate. Yet, the overall form is close to one that has perfect symmetry. Our two hands are also almost anatomically perfect; they mirror images of each other, but they are noticeably asymmetrical with regard to function, or physiology. So, we can conjure up of a vision of the left being a reversal of the right — its mirror image. However, the moment we begin to use words like mirro image, we are ushering in the idea of one shape that corresponds to the other. The point is — it is unlike reflection, which is a mathematical concept. The best part is reflections capture symmetries — from the human body to the petals of a flower. The brain [cerebrum] too is symmetrical; it consists of right and left hemispheres.

What about symmetry in plants, one may well ask. As integrative biologist Frederick Essig explains, "Plants don't move, so symmetry would have a different meaning, if it exists at all. In fact, it does, but it's more complicated. Plants exhibit both radial symmetry and bilateral symmetry, often at the same time. In flowers, it has a lot to do with pollination. A sunflower head has radial symmetry, allowing small insects to land on top, while a snapdragon flower has bilateral symmetry, inviting large bees to enter from the side."

He elaborates, "The whole plant can have one or both symmetries also — as discussed by naturalist Francis Halle. Plants that are anchored to a single spot, like trees, exhibit an overall symmetry that is roughly radial. The weight is more-or-less evenly balanced around its central axis, which extends down the trunk into a woody taproot system. A tree could hypothetically be spun around its central axis without affecting its environmental orientation. Like a coral polyp, a tree gathers resources — sunlight and carbon dioxide — that are widely dispersed, and so must spread a wide net from its central trunk. The symmetry may not be exact because of the random nature of tree branching, but overall the crown of a typical tree is a rounded dome. This symmetry is more obvious and exact in something like a tree fern or a single-stemmed palm tree, like a date palm, albeit they do not have woody taproot systems."

Nature presents symmetries on a large scale. Let’s cull an example: a developing frog embryo. The embryo begins life as a spherical cell. It soon loses symmetry as it divides, until it has become a blastula. Back again. Its overall form is now spherical. After that, the symmetry is broken yet again and only a single mirror symmetry is retained, leading to the bilateral symmetry of the adult. You’d call it a frog-leap to symmetry.

The frog narrative is, of course, an example in isolation, because there are any number of them based on a general principle which celebrates the symmetrical raison d’être. Symmetry breaking is also one such principle. Yet, in order for symmetry to break, it has to be present to start with. Writes mathematician Ian Stewart, “This is all very well, but it produces a deep paradox.” He adds, “If the laws of physics are the same at all places and at all times, why is there any interesting structure in the universe at all?”

He also demystifies Curie’s principle, touched upon earlier. Curie’s credo, he observes, is not flawless. It offers, for instance, a misleading intuition about how a symmetric system should behave. A much better principle, according to Stewart, is the exact opposite — the system of spontaneous symmetry breaking. Most of nature’s symmetric patterns arise out of a certain version of this general mechanism. Which also, in more ways than one, rehabilitates Curie’s principle — if only we permit tiny asymmetric disturbances that can trigger instability of the fully symmetric state.

Curie’s idea cannot, perforce, answer tiny departures — for the prediction of symmetries — because it is envisages them. Yet, it is an informative model for a real system with perfect symmetry. As Stewart explains, “One of the more puzzling types of symmetry in nature is mirror symmetry, symmetry with respect to a reflection. Mirror symmetries of three-dimensional objects cannot be realised by turning the objects in space — a left shoe cannot be turned into a right shoe by rotating it.” He elaborates, “Yet, the laws of physics are nearly mirror-symmetric, the exceptions being certain interactions of subatomic particles. As a result, any molecule that is not mirror-symmetric potentially exists in two different forms — left- and right-handed, so to speak.”

Yet another outstanding paradigm would be the bees’ honeycomb, with its hexagonal stiles. Which brings us to one monumental question: where do symmetries of natural patterns come from? Toss a pebble into a pond, and you’ll know. A simple thing to do, really. But, it has a wondrous modicum of expression by way of a universal truth: the ripples on a pond are examples of broken symmetry. Not wholly, may be -— and, that’s why we always see a pattern. Of patterns by way of circular ripples, one quite distinct from the other, depending upon the point of impact.

Creating symmetrical synchrony within our environment has been our second nature, since the dawn of time, notwithstanding transgressions, thanks to scientific and technological advance. Take for example, the ancient Chinese art of geomancy, or feng shui [pronounced ‘fung shway’], that has in it the wherewithal to create balance and harmony in our personal environment. Feng shui, in Chinese, means wind and water. The wind provides the movement or flow of universal energy or ‘chi’ which affects everything; water provides the container or receiver of ‘chi.’ Feng shui, in précis, is a time-honoured system of rules, concepts, and principles — it also explains how our lives are pragmatically and spiritually linked to our environment.

Physicists now recognise four fundamental forces in nature; gravity, electromagnetism, and strong and weak nuclear interactions. It is known that the weak force violates mirror symmetry — that is, it behaves differently in left- and right-handed versions of the same physical problem. However this may be, current theories explain that the four fundamental forces of physics became unified — that is, symmetrically related — at extremely high energy levels prevailing in the early universe. Yet, we don’t live in it. Still.

Stewart expands the analogy, “Our universe could have been different; it could have been any of the other universes that, potentially, could arise by breaking symmetry in a different way. That’s quite a thought. But, there is an even more intriguing thought: the same basic method of pattern formation, the same mechanism of symmetry breaking in a mass-produced universe, governs the cosmos, the atom, and us.” May be, you’d evoke Albert Einstein’s famous aphorism that “God does not play dice with the universe.” Yet another allegory would be what quantum physicist Wolfgang Pauli summed up, “The Lord is a weak Ieft-hander.”